{"id":"https://openalex.org/W3177949702","doi":"https://doi.org/10.3233/jifs-210717","title":"(\u03b1, \u03b2)-Multi-granulation bipolar fuzzified rough sets and their applications to multi criteria group decision making","display_name":"(\u03b1, \u03b2)-Multi-granulation bipolar fuzzified rough sets and their applications to multi criteria group decision making","publication_year":2021,"publication_date":"2021-07-10","ids":{"openalex":"https://openalex.org/W3177949702","doi":"https://doi.org/10.3233/jifs-210717","mag":"3177949702"},"language":"en","primary_location":{"id":"doi:10.3233/jifs-210717","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jifs-210717","pdf_url":null,"source":{"id":"https://openalex.org/S179157397","display_name":"Journal of Intelligent & Fuzzy Systems","issn_l":"1064-1246","issn":["1064-1246","1875-8967"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent &amp; Fuzzy Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023804984","display_name":"Rizwan Gul","orcid":"https://orcid.org/0000-0002-6139-1872"},"institutions":[{"id":"https://openalex.org/I12469534","display_name":"Quaid-i-Azam University","ror":"https://ror.org/04s9hft57","country_code":"PK","type":"education","lineage":["https://openalex.org/I12469534"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Rizwan Gul","raw_affiliation_strings":["Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan","institution_ids":["https://openalex.org/I12469534"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078902055","display_name":"Muhammad Shabir","orcid":"https://orcid.org/0000-0002-3161-8482"},"institutions":[{"id":"https://openalex.org/I12469534","display_name":"Quaid-i-Azam University","ror":"https://ror.org/04s9hft57","country_code":"PK","type":"education","lineage":["https://openalex.org/I12469534"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Shabir","raw_affiliation_strings":["Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan","institution_ids":["https://openalex.org/I12469534"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023804984"],"corresponding_institution_ids":["https://openalex.org/I12469534"],"apc_list":null,"apc_paid":null,"fwci":0.2959,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.60535057,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"41","issue":"1","first_page":"2025","last_page":"2060"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11063","display_name":"Rough Sets and Fuzzy Logic","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9320999979972839,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/rough-set","display_name":"Rough set","score":0.9273282289505005},{"id":"https://openalex.org/keywords/granulation","display_name":"Granulation","score":0.8021935224533081},{"id":"https://openalex.org/keywords/granular-computing","display_name":"Granular computing","score":0.5390855669975281},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5352281928062439},{"id":"https://openalex.org/keywords/fuzzy-set","display_name":"Fuzzy set","score":0.5162046551704407},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.510758638381958},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.48101311922073364},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.47870591282844543},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.45918577909469604},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4152945876121521},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35803934931755066},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.355709969997406},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2811048626899719},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.06391763687133789}],"concepts":[{"id":"https://openalex.org/C111012933","wikidata":"https://www.wikidata.org/wiki/Q3137210","display_name":"Rough set","level":2,"score":0.9273282289505005},{"id":"https://openalex.org/C88463166","wikidata":"https://www.wikidata.org/wiki/Q1543243","display_name":"Granulation","level":2,"score":0.8021935224533081},{"id":"https://openalex.org/C17209119","wikidata":"https://www.wikidata.org/wiki/Q5596712","display_name":"Granular computing","level":3,"score":0.5390855669975281},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5352281928062439},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.5162046551704407},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.510758638381958},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.48101311922073364},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.47870591282844543},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.45918577909469604},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4152945876121521},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35803934931755066},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.355709969997406},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2811048626899719},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.06391763687133789},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/jifs-210717","is_oa":false,"landing_page_url":"https://doi.org/10.3233/jifs-210717","pdf_url":null,"source":{"id":"https://openalex.org/S179157397","display_name":"Journal of Intelligent & Fuzzy Systems","issn_l":"1064-1246","issn":["1064-1246","1875-8967"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Intelligent &amp; Fuzzy Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.7799999713897705,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":69,"referenced_works":["https://openalex.org/W35369483","https://openalex.org/W1129958558","https://openalex.org/W1542837303","https://openalex.org/W1551588360","https://openalex.org/W1554773601","https://openalex.org/W1580419169","https://openalex.org/W1751558718","https://openalex.org/W1754863686","https://openalex.org/W1964660891","https://openalex.org/W1965795249","https://openalex.org/W1973688644","https://openalex.org/W1976555061","https://openalex.org/W1978352585","https://openalex.org/W1986839581","https://openalex.org/W1995275854","https://openalex.org/W1999693983","https://openalex.org/W2005739429","https://openalex.org/W2007620983","https://openalex.org/W2013217210","https://openalex.org/W2032972115","https://openalex.org/W2042560256","https://openalex.org/W2049157258","https://openalex.org/W2066150658","https://openalex.org/W2069125985","https://openalex.org/W2069754181","https://openalex.org/W2074145995","https://openalex.org/W2074193720","https://openalex.org/W2078032741","https://openalex.org/W2083267403","https://openalex.org/W2090660539","https://openalex.org/W2105012045","https://openalex.org/W2107566963","https://openalex.org/W2143451122","https://openalex.org/W2155294756","https://openalex.org/W2162755671","https://openalex.org/W2170755382","https://openalex.org/W2172368975","https://openalex.org/W2196468142","https://openalex.org/W2321837546","https://openalex.org/W2339499216","https://openalex.org/W2463945886","https://openalex.org/W2512214103","https://openalex.org/W2586356223","https://openalex.org/W2602688464","https://openalex.org/W2607421718","https://openalex.org/W2796019338","https://openalex.org/W2805543191","https://openalex.org/W2884022287","https://openalex.org/W2887485161","https://openalex.org/W2888870504","https://openalex.org/W2890144670","https://openalex.org/W2917046450","https://openalex.org/W2919397193","https://openalex.org/W2973841086","https://openalex.org/W2981506493","https://openalex.org/W2982471993","https://openalex.org/W3007593690","https://openalex.org/W3033560154","https://openalex.org/W3038373120","https://openalex.org/W3040745443","https://openalex.org/W3109761444","https://openalex.org/W3132686745","https://openalex.org/W3149320479","https://openalex.org/W4211007335","https://openalex.org/W4255833381","https://openalex.org/W6658964965","https://openalex.org/W6683098079","https://openalex.org/W6693091319","https://openalex.org/W6704185492"],"related_works":["https://openalex.org/W154269579","https://openalex.org/W2085182244","https://openalex.org/W2766401420","https://openalex.org/W2376448076","https://openalex.org/W2547843415","https://openalex.org/W2917046450","https://openalex.org/W2095731367","https://openalex.org/W3005671167","https://openalex.org/W2283513923","https://openalex.org/W3146518063"],"abstract_inverted_index":{"Pawlak\u2019s":[0],"rough":[1,13,20,30,45,76,88,104,172],"set":[2,14,21,31,46,173],"theory":[3,22,158],"based":[4,200],"on":[5,201],"single":[6],"granulation":[7],"has":[8,23,59],"been":[9,60],"extended":[10],"to":[11,143,195],"multi-granulation":[12],"structure":[15],"in":[16,29,123,159],"recent":[17],"years.":[18],"Multi-granulation":[19],"become":[24],"a":[25,52,110,192,213],"flouring":[26],"research":[27],"direction":[28],"theory.":[32],"In":[33,62,141],"this":[34,50,157,208],"paper,":[35],"we":[36,67,190,221],"propose":[37],"the":[38,63,82,94,98,128,175,179,205,218],"notion":[39],"of":[40,54,65,71,112,118,177,181,185,207],"(\u03b1,":[41,72,84,100,129,131,135,168,202],"\u03b2)-multi-granulation":[42,73,85,101,169],"bipolar":[43,55,74,86,102,170],"fuzzified":[44,75,87,103,171],"((\u03b1,":[47,90,106],"\u03b2)-MGBFRSs).":[48],"For":[49],"purpose,":[51],"collection":[53],"fuzzy":[56],"tolerance":[57],"relations":[58],"used.":[61],"framework":[64],"multi-granulation,":[66],"proposed":[68,119,146],"two":[69],"types":[70],"sets":[77,89,105],"model.":[78],"One":[79],"is":[80,96,210],"called":[81,97],"optimistic":[83],"\u03b2)":[91,107,132,136],"o-MGBFRSs)":[92],"and":[93,116,134,183,204],"other":[95],"pessimistic":[99],"p-MGBFRSs).":[108],"Subsequently,":[109],"number":[111],"important":[113,164],"structural":[114],"properties":[115],"results":[117],"models":[120],"are":[121,138,150,153,187],"investigated":[122],"detail.":[124],"The":[125],"relationships":[126],"among":[127],"\u03b2)-MGBFRSs,":[130,203],"o-MGBFRSs":[133],"p-MGBFRSs":[137],"also":[139,222],"established.":[140],"order":[142],"illustrate":[144],"our":[145],"models,":[147],"some":[148],"examples":[149],"considered,":[151],"which":[152],"helpful":[154],"for":[155],"applying":[156],"practical":[160,214],"issues.":[161],"Moreover,":[162],"several":[163],"measures":[165],"associated":[166],"with":[167,217],"like":[174],"measure":[176,180],"accuracy,":[178],"precision,":[182],"accuracy":[184],"approximation":[186],"presented.":[188],"Finally,":[189],"construct":[191],"new":[193],"approach":[194],"multi-criteria":[196],"group":[197],"decision-making":[198],"method":[199],"validity":[206],"technique":[209],"illustrated":[211],"by":[212],"application.":[215],"Compared":[216],"existing":[219],"results,":[220],"expound":[223],"its":[224],"advantages.":[225]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
